Question: Reduce to lowest terms: $- \dfrac{5}{3} \div \dfrac{9}{2} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{9}{2}$ is $ \dfrac{2}{9}$ Therefore: $ - \dfrac{5}{3} \div \dfrac{9}{2} = - \dfrac{5}{3} \times \dfrac{2}{9} $ $ \phantom{- \dfrac{5}{3} \times \dfrac{2}{9}} = \dfrac{-5 \times 2}{3 \times 9} $ $ \phantom{- \dfrac{5}{3} \times \dfrac{2}{9}} = \dfrac{-10}{27} $